ANEJO Nº5 HIDROLOGÍA Y
3. DESCRIPCIÓN DE LA RED
3.5.4.1 Calculation of bulk flow viscosity
In order to apply Newtonian flow lengthening models to the Cordón Caulle lava, the bulk flow viscosity must first be estimated using Table 3.6 (Jeffreys, 1925). We use a
lava density of 2300 kg m-3 (Castro et al., 2013), a flow depth of ~30 m at the flow front
(Farquharson et al., 2015), a slope of 7˚ (determined from a pre-eruption Aster DEM along the length of the southern flow, Appendix 8A.19), and n = 2 for flow in a wide channel (Hulme, 1974; Stevenson et al., 2001; Harris et al., 2004; Farquharson et al., 2015).
In order to determine the lava flow surface velocity, surface features in the main channel of the flow (ogives, fractures in the flow crust, and pale pumice rafts) were tracked between two georeferenced satellite images taken in 9 October 2011 and 26 January 2012 (locations of the measurements are shown in Fig. 3.8). Surface velocities of 2.2-6.2×10-5 m s-1 were derived (mean 3.8×10-5 m s-1), giving a viscosity range of
2.0-5.6×1010 Pa s (mean 3.6×1010 Pa s). Here we assume that the surface velocity is
comparable to the core velocity, which may not be the case if the crust is experiencing drag against the levées.
3.5.4.2 Models of flow lengthening
Due to the northern flow being topographically constrained at its front, lava flow advance models are only relevant to the initial advance of the southern flow. We assume that the lava flow was initially controlled by either a Newtonian or non- Newtonian bulk rheology for the first 75 to 127 days (first identification of ogives and surface fractures respectively). Henceforth, the presence of ogives and surface fractures indicate that surface crust had attained sufficient thickness and strength to exert a controlling influence on flow behaviour. Model results should be disregarded for periods after the southern flow front began to interact with a topographic barrier (202 days). However, by this time the major changes in rheological control had already occurred, with the lava firmly in the crustal-control regime and breakouts forming at many points around the lava flow. The effusion rates (Table 3.3) are cited for the entire flow field (Bertin et al., 2015). As a best estimate, we assume that the north and south
flow branches were fed approximately equally – i.e. each at half the rate given in Table 3.3.
Models based on the fixed parameter approach (Eq. 3.1 and 3.2, utilising values in Table 3.2) underestimate final lava flow length by ~1500 – 1000 m for transitions from viscosity to crustal control after 75 and 127 days respectively (Fig. 3.9A). The biggest disparity is in the early stages of the eruption, when the observed lava flow advance rate far exceeded model predictions, suggesting that early-erupted lava was substantially less viscous than the later-erupted lava for which we have viscosity estimates (Farquharson et al. 2015). Such increases in the lava flow viscosity with time likely relate to cooling, degassing and crystallisation of the lava flow.
Models that employ the flexible parameter approach (Eq. 3.3 and 3.4, Eq. 3.4 and 3.5) and assume a core yield strength control underestimate the final flow length by ~2000 m (Fig. 3.9B). When an initial viscosity control and 75 day crustal control transition are used the final lava flow length is underestimated by ~900 m. However, when the crustal control transition occurs after 127 days, the modelled final lava flow length closely fits with observed values, showing the importance of constraining the timing of model transitions. Not surprisingly, the flexible parameter approach provides a better fit for the early stages of the lava evolution than the fixed parameter approach, because it accounts for variations in lava flow properties, such as the flow width.
3.5.4.3 Inferring Cordón Caulle flow properties
The Cordón Caulle lava flow gained most of its length in the first two to three months of the eruption, during inferred viscosity-controlled advance. However, reliable viscosity estimates could only be made from the latter stages of the eruption when recognisable surface features could be tracked and the flow was less obscured by the eruption plume. Thus, viscosity estimates are upper bounds because they are likely to be affected by the presence of a crust, and the later lava was likely cooler, more degassed and more crystalline than during the earlier stages (Schipper et al., 2015). Flow length models offer an alternative approach to constrain plausible values of flow viscosity, crust yield strength and internal yield strength.
The optimised fixed parameter model provides a best fit to observed flow lengthening for a viscosity of 3.3×109 Pa s, a crustal yield strength of 2.5×108 Pa and a transition
from viscosity to crustal control after 60 days (Fig. 3.10A). This lower viscosity, an order
Figure 3.9: Modelled and actual flow length changes of the 2011 Cordón Caulle rhyolite lava flow. The black arrow shows the time at which the flow starts to interact with a topographic barrier. (A) Results from fixed parameter approach (Eq. 3.1 and 3.2) assuming the flow is initially controlled by its viscosity and then by the strength of a brittle crust. (B) Results from flexible parameter approach (Eq. 3.3 and 3.4, and Eq. 3.5 and 3.4) assuming the flow is initially controlled by either its viscosity or internal yield strength.
of magnitude less than estimates for later lava (Farquharson et al. 2015), could be representative of initially effused lava that was hotter, less crystalline and more volatile- rich. A viscosity value can also be estimated directly using the Einstein-Roscoe equation:
𝜂 = 𝜂0(1 − 𝑅Φ)−𝑄 , [𝐸𝑞. 3.7]
where η0 is the melt viscosity which is determined here from Giordano et al. (2008), R and Q are constants equal to 1.67 and 2.5 respectively, and Φ is the crystal packing fraction. Using an eruptive temperature of 900 ˚C, a melt composition from Schipper et al. (2015) with a volatile content of 0.1%, and an initial crystal content of up to ~30 volume% at the vent (Schipper et al., 2015) gives a viscosity of ~1.5×109 Pa s. This is
in close agreement to the fixed parameter model suggested here (Eq. 3.1 and 3.2, Fig. 3.10A). We acknowledge that the Einstein-Roscoe equation is based on the assumption that the crystal population is isotropic. However, in the Cordón Caulle flow most crystals are rod-like microlites (Schipper et al., 2015), and such high aspect ratio crystals increase the magma viscosity more strongly than isotropic crystals (Mueller et al., 2011; Mader et al., 2013). Accordingly, this estimate could be taken as a minimum value, and viscosity likely increased with time due to degassing and crystallisation of the lava flow. Alternatively, the alignment of an initial randomly orientated microlite population could lead to shear thinning behaviour during lava flow emplacement and a reduction in apparent viscosity. Despite these limitations, the value independently derived from the Einstein-Roscoe equation does support the viscosity value derived through the optimised lava flow models, Eq. 3.1 and 3.2.
Optimising a flexible parameter model with Newtonian viscosity and subsequent crustal control (Eq. 3.3 and 3.4) gives the observed best fit to the actual flow lengthening for a rather higher viscosity of 1×1010 Pa s, a lower crustal yield strength of 4×107 Pa and a
similar flow control transition time of 50 days (Fig. 3.10B). A flexible parameter model that assumes initial core yield strength control provides best fit for a core yield strength of 9.8×104 Pa, a crustal yield strength of 4×107 Pa and a transition in flow control at 50
days. As these models are inherently non-unique and other combinations of flow properties and transition time in flow control can yield equally good fits to observations, it is valuable to compare the determined flow parameters to previously published results. The inferred values of crustal yield strength correspond with those proposed in other studies of silicic lava flows and domes, 106 – 107 Pa (Griffiths and Fink, 1993;
DeGroat-Nelson et al., 2001) and the lower core yield strength determined here is in line with other estimations of high-silica content lava yield strength (Blake, 1990; Fink and Griffiths, 1998). The inferred viscosity from the idealised flexible parameter approach (Eq. 3.3 and 3.4, Fig. 3.10B) is in line with the lower viscosities calculated
Figure 3.10: Model results for the Cordón Caulle lava flow. The black arrow shows the time at which the flow starts to interact with a topographic barrier. (A) Fixed parameter approach (Eq. 3.1 and 3.2) where flow properties have been inferred from the best fit of the applied models. (B) Flexible parameter approach (Eq. 3.3 and 3.4, and 3.5 and 3.4) where flow properties have been inferred from the best fit of the applied model.
using Jeffreys (1925) by Farquharson et al. (2015), based on velocities determined from structure-from-motion photogrammetry of breakouts (1.21×1010 to 4.01×1010 Pa
s) from the flow margin. This viscosity value is slightly lower than the inferred bulk lava viscosity determined from satellite observations.
3.5.4.4 Model sensitivities
The uncertainties associated with model input result in uncertainties in model outputs; for example varying slope angle by 2˚ in all models leads to final flow length changes of ~2 – 10%, corresponding to flow length variations up to a few hundred metres. However, variations due to uncertainties in crustal yield strength and flow viscosity are much greater. Applying the range of viscosity values derived from initial range in flow channel velocities leads to a range in the final modelled flow lengths of ~1.5 km for the fixed parameter approach (Fig. 3.11A) and 2 km for the flexible parameter approach (Fig. 3.11B).
Previously published values for the crustal yield strength of silicic lavas range from 106
to 108 Pa (Griffiths and Fink, 1993; Bridges, 1997; Fink and Griffiths, 1998; DeGroat-
Nelson et al., 2001; Kerr and Lyman, 2007; Castruccio et al., 2013). Reducing the crustal yield strength by an order of magnitude to 107 Pa in the fixed parameter
approach (Eq. 3.1 and 3.2) produces a significant increase in modelled lava flow advance rate in the crustal control regime (Fig. 3.11C) compared to the original model (Fig. 3.9A), and increases the final lava flow length by >1.5 km. An earlier transition in flow control (at day 75), results in a longer lava flow than when the transition occurs after 127 days. This is because at this time in the modelled scenario, the crust provided a lesser retarding force than the flow viscosity, leading to accelerated lava advance rates upon flow control transition. In reality though, the lava flow would have retained the viscous retardation and remained viscosity controlled until the crust became
sufficiently strong to dominate over the viscous forces. Thus, this apparent increase in lava flow advance is an artefact of the modelling approach that considers rheological controls in isolation rather than combination. The effect on the flexible parameter models of lowering crust yield strength (Eq. 3.3 and 3.4) is not as pronounced (Fig.
Figure 3.11: Model results for the Cordón Caulle lava flow. The black arrow shows the time at which the flow starts to interact with a topographic barrier. (A) Range of model results when viscosity is varied using the fixed parameter approach (Eq. 3.1 and 3.2). The red area represents a transition in rheological control after 127 days and the grey area represents a transition after 75 days. Dashed lines show the high and low-viscosity end members and the solid lines show the mean viscosity. (B) Similar to (A) but for a flexible parameter approach (Eq. 3.3 and 3.4). (C) Fixed parameter approach (Eq. 3.1 and 3.2) where the crust yield strength is reduced by an order of magnitude to 107 Pa. (D) Similar to
(C) but for a flexible parameter approach (Eq. 3.3 and 3.4 or Eq. 3.5 and 3.4). Flow is initially controlled by either its viscosity or core yield strength. Two core yield strength curves give similar results for a transition in control after 75 days and 127 days.
3.11D), but leads to an increase in the final flow length compared to the original model (Fig. 3.9B), and provides a closer fit to the actual flow lengthening.
3.6 Discussion
Field and remote sensing observations, as well as straightforward flow advance models, suggest that both the 2001 Etna basaltic flow and the 2011-2012 Cordón Caulle rhyolitic lava flow were controlled in their latter stages by a cooled crust after an initial viscous control. The cooled crust acted to retard the lava flows, ultimately halting them before breakouts formed at the flow front and along flow margins (Behncke and Neri, 2003; Coltelli et al., 2007; Applegarth et al., 2010c; Tuffen et al., 2013).